Two Equations in Standard Form

Linear equation is an algebraic equation which has constants and variables together. Linear equation has 1 or more variables. Linear equation has more forms. Standard form is one of the form of linear equation.

Standard form of linear equation is Ax + By = C.

Here A, B and C are constants. X and y are variables. A and B are not zero.

We can solve standard form of equation using substitution or elimination method. But here we use two standard form equations. Let us see how to solve.

Please express your views of this topic sample standard deviation formula by commenting on blog.

Standard Form of Two Equations – Substitution Method:

Problem:

Solve these two standard forms of equation using substitution method.

2x + 4y – 12 = 0

X – 2y – 4 = 0

Solution:

The given standard form of two equations are,

2x + 4y = 12  (1)

X – 2y = 4  (2)

From (2), we rewrite the equation as

X = 4 + 2y  (3)

Substitute equation (3) into (1) to find the variable y.

2(4+2y) + 4y = 12

Apply the distributive property, we get

8 + 4y + 4y = 12

Combine like terms,

8+ 8y = 12

Subtract 8 from each side.

8 – 8 + 8y = 12 – 8

8y = 4

Divide by 8 each side.

`(8y)/8` = `4/8`

Y = `1/2`

Substitute y = `1/2` into equation (2)

X – 2y = 4

X – 2(`1/2` ) = 4

X – 1 = 4

Add 1 to each side.

X – 1 + 1 = 4 + 1

X = 5.

Therefore, the solutions are 5 and 1/2.

I am planning to write more post on Different Types of Graphs and Charts and Different Types of Pyramids. Keep checking my blog.

Standard Form of Two Equations – Elimination Method:

Problem :

Use elimination method to determine the solutions of the following the systems of equations.

x + y – 16 = 0 and 4x – 2y – 4 = 0

Solution:

The given standard forms of two equations are

x + y = 16  (1)

4x – 2y = 4  (2)

Step 1:

Multiply the equation (1) by 2 and Equation (2) by 1 to get the coefficients of variable y same. So the equations are,

2x + 2y = 32

4x – 2y = 4

Step 2:

Add the two equations for eliminating y variable.

2x + 2y + 4x – 2y = 32 + 4

2x + 4x + 2y – 2y = 36

6x = 36

Divide by 6 both sides.

x = 6

Step 3:

Substitute the x value into the equation (1) to get value of y variable.

x + y = 16

6 + y = 16

Subtract 6 from each side.

y = 10.

The solutions are x = 6 and y = 10.